Example Card: Solving $x^2 = a$
Master Solving $x^2 = a$ for Grade 9 math with step-by-step practice. How can a simple quadratic equation have two different answers?
Key Concepts
How can a simple quadratic equation have two different answers? Let's see how taking a square root reveals both solutions.
Example Problem Solve the equation $x^2 = 121$.
Step by Step 1. We start with the given equation where the variable is already squared and isolated. $$x^2 = 121$$ 2. Take the square root of both sides. Remember to include both the positive and negative roots on the right side. $$ \sqrt{x^2} = \pm\sqrt{121} $$ 3. Simplify the square roots to find the two possible values for $x$. $$ x = 11 \quad \text{or} \quad x = 11 $$ 4. We can write the final solution using the plus minus symbol. $$ x = \pm 11 $$ 5. Check both solutions : $$ \begin{aligned} x^2 &= 121 \\ 11^2 &\stackrel{?}{=} 121 \\ 121 &= 121 \quad \checkmark \end{aligned} \quad \begin{aligned} x^2 &= 121 \\ ( 11)^2 &\stackrel{?}{=} 121 \\ 121 &= 121 \quad \checkmark \end{aligned} $$.
Common Questions
What is Solving $x^2 = a$ in Algebra 1?
Solving $x^2 = a$ is a core Grade 9 Algebra 1 concept covering properties and applications.
How do you work with Solving $x^2 = a$ in Grade 9 math?
Hey! Solving equations like is like a fun detective game. You're looking for a secret number that, when multiplied by itself, gives you 121. The big twist is that there are usually two secret numbers that work! Think about it: A positive number times itself is positive: . A negative number times its.
What are common mistakes when learning Solving $x^2 = a$?
Hey! Solving equations like is like a fun detective game. You're looking for a secret number that, when multiplied by itself, gives you 121. The big twist is that there are usually two secret numbers that work! Think about it: A positive number times itself is positive: . A negative number times itself is also positive: . So, to find all the soluti.